# A fixed-parameter algorithm for the directed feedback vertex set problem

Chen, J. and Liu, Y. and Lu, S. and O'Sullivan, B. and Razgon, Igor
(2008)
A fixed-parameter algorithm for the directed feedback vertex set problem.
In:
UNSPECIFIED (ed.)
*Proceedings of the fourtieth annual ACM symposium on Theory of computing.*
New York, USA:
ACM Publications, pp. 177-186.
ISBN 9781605580470.

## Abstract

The (parameterized) feedback vertex set problem on directed graphs, which we refer to as the dfvs problem, is defined as follows: given a directed graph G and a parameter k, either construct a feedback vertex set of at most k vertices in G or report that no such set exists. Whether or not the dfvs problem is fixed-parameter tractable has been a well-known open problem in parameterized computation and complexity, i.e., whether the problem can be solved in time f(k)nO(1) for some function f. In this paper we develop new algorithmic techniques that result in an algorithm with running time 4k k! nO(1) for the dfvs problem, thus showing that this problem is fixed-parameter tractable.

## Metadata

Item Type: | Book Section |
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School: | School of Business, Economics & Informatics > Computer Science and Information Systems |

Depositing User: | Sarah Hall |

Date Deposited: | 01 Aug 2013 16:26 |

Last Modified: | 01 Aug 2013 16:26 |

URI: | https://eprints.bbk.ac.uk/id/eprint/7933 |

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